Business-school professor Garold Lantz travels to Asian universities several times a year and earns about 30,000 United Airlines miles on each trip. Starting next year, his mileage reward from United will plummet to about 12,000 miles a trip. He may take the same trips as before, but he’s considering paying United’s partner Singapore Airlines to get more miles.

“I anticipate switching as my resentment builds,” says Mr. Lantz, a McGowan School of Business marketing and international business professor at Kings College in Wilkes-Barre,...